This paper deals with the operation .9R 'of symmetric decreasing re-arrangement which maps Wl,p (Rn) to Wi ,p (Rn) . We show that even thoughit is norm decreasing, .9R is not continuous for n ~ 2. The functions at which.9R is continuous are precisely characterized by a new property called co-arearegularity. Every sufficiently differentiable function is co-area regular, and both<...

Disjunctive Logic Programming (DLP) under the consistent answer set semantics is an advanced formalism for knowledge representation and reasoning. It is, under widely believed assumptions, strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. However, this higher expressiveness comes at a computational cost, and...

We establish the complexity of decision problems associated with the nonmonotonic modal logic S4. We prove that the problem of existence of an S4-expansion for a given set A of premises is P 2-complete. Similarly, we show that for a given formula ' and a set A of premises, it is P 2-complete to decide whether ' belongs to at least one S4-expansion for A, and it is P 2-complete to decide whether...